Reverse Mortgage Design

Reverse Mortgage Design

Jo?o F. Cocco

Paula Lopes

This version: March 2015

ABSTRACT

We study the role of housing wealth for the financing of retirement consumption, focusing on the design of the financial products that allow households to tap into their home equity. Our model results show that bequest and precautionary savings motives have difficulty generating the high homeownership rates late in life observed in U.S. data. The model is more successful at matching the data, including a limited demand for reverse mortgages, when: (i) retirees value property maintenance less than potential buyers of the property; (ii) for psychological reasons, retirees derive utility from remaining in the same house. We use the model to evaluate the impact of different reverse mortgage features and costs on their benefits to retirees, cash-flows to lenders and to the government agency that provides mortgage insurance.

JEL classification: G21, E21. Keywords: Household finance, reverse mortgages, retirement, housing wealth.

Department of Finance, London Business School, Centre for Economic Policy Research, Center for Financial Studies, and Netspar.

Department of Finance, London School of Economics and Netspar. We would like to thank Magnus Dahlquist, Francisco Gomes, Thomas Post and seminar participants at Berkeley, Glasgow, Kent, Maastricht, McGill, the Sveriges Riksbank, and the Netspar International Pension Workshop for comments.

1 Introduction

In many countries the government, through the social security system, provides a pension to retirees. However, recently there have been increasing concerns about the sustainability of these (mainly unfunded) social security systems and the adequacy of households' private retirement savings (Scholz, Seshadri, and Khitatrakun, 2006).1 Our paper studies the role of housing wealth for the financing of retirement consumption, focusing on the design of the financial products that allow retired households to tap into their home equity.

Our motivation for studying the role of housing wealth is straightforward: homeownership rates are particularly high among U.S. households and for most of them housing assets constitute the single most important component of their wealth (Bertaut and Starr-McCluer, 2002). Retirees could release their home equity by downsizing, moving into rental accommodation, or by using financial products such as reverse mortgages. However, in spite of its potentially large relevance, the existing empirical studies do not find strong support for housing wealth being used to finance non-housing retirement consumption. Retirees do not appear to purchase a house of lower value or to discontinue homeownership. The few that discontinue homeownership do so only late in life (after age 75 or so as documented by Venti and Wise, 2001, Poterba, Venti, and Wise, 2011a). To date the demand for reverse mortgages has been limited (Caplin, 2002, Davidoff, 2014).

The explanations that have been proposed in the literature for why older individuals do not wish to dissave could in principle also explain why they do not wish to tap into their home equity. The ones which have received more attention are bequest motives (Bernheim, 1991) and precautionary saving motives arising from uncertain life span and risky medical expenditures (Palumbo, 1999, De Nardi, French, and Jones, 2010). If retirees do not wish to dissave they may not want to sell their house or to borrow against it. It may also be re-assuring for retirees to know that if they remain homeowners they have an hedge against future house price fluctuations (Sinai and Souleles, 2005).

In order to investigate these explanations we build a model of the consumption and housing choices of retired homeowners. In our model retirees derive utility from housing, non-durable consumption and from leaving a bequest. They are subject to several sources of risk including an uncertain life span, health risk, medical expenditure shocks, interest rate risk and house price fluctuations. Our analysis is quantitative so that we use several data sources to parameterize these risks. The focus in the first part of the paper is positive. The question is whether, given the pension income and assets of retired homeowners and the

1This is in part due to the aging of the population: the ratio of the number of U.S. individuals aged 18 to 64 to those aged 65 or over is projected to decline from 4.84 in 2010 to 2.96 by 2030 (Source: Projections of the Population by Selected Age Groups and Sex for the United States: 2010 to 2050, U.S. Census Bureau). The U.S. Social Security trust fund assets are expected to be exhausted by 2036 (2011 OASDI Trustees Report).

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risks that they face, the model can generate homeownership and saving decisions that match those of past generations of retired homeowners, observed in the Health and Retirement Study (HRS), and a limited demand for reverse mortgages.

The model results show that even though a bequest motive or a precautionary savings motive lead individuals to remain homeowners until a later age, the decline in homeownership rates with age is still too large compared with the data. The fundamental economic reason is simple. Even though precautionary savings and bequest motives lead retirees to save more, housing is not an asset that is particularly suitable for this purpose, since it is lumpy and risky. As retirees age, as they are hit by health and medical expenditure shocks, and as house prices and interest rates fluctuate, the likelihood that at all points in time the value of the retirees' house matches the amount that they wish to consume of housing and to save is fairly small. As a result, and in the model, many of them decide to sell their house too soon compared to the data. We show that simply making bequest or precautionary motives stronger does not address this issue. They lead to higher savings in old age, but not necessarily in housing, so that matching the composition of savings is difficult.

In an attempt to match the data, we motivate and model two alternative features. The first is that retirees value property maintenance less than potential buyers of the house, so that a reduction in maintenance expenses has a larger effect on its price than on the utility that retirees derive from it. For example, retirees may not value a new kitchen in the same way as potential buyers of the property. Davidoff (2005) provides evidence that retirees reduce housing maintenance.2 The second is that retirees derive some utility benefits from living in the same house in which they retired, possibly because their house brings good memories or because they know their next door neighbors. These two explanations are related, in that they introduce a wedge between the utility value of the house for the retiree and its value from the perspective of a buyer of the property. But they have different cash-flow and wealth dynamics implications, that are relevant for the benefits from and the design of reverse mortgages.

Reverse mortgages allow retired homeowners to withdraw home equity without moving and to make partial withdrawals which may help them choose a savings level that better matches their desired level. They are available in several countries, including the U.S. where they benefit from government guarantees, but to date the demand for them has been limited. Figure 1 plots the number of reverse mortgage loans endorsed by the Federal Housing Administration (FHA) and the S&P/Case-Shiller 10-City Composite Price Index over the last three decades. The number of new reverse mortgages increased considerably over this period to a monthly maximum of 12,000 just before the onset of the recent financial

2This reduction could also be due to retirees not having the financial resources needed to maintain the property and that a reduction in maintenance is valued equally by retirees and potential buyers of the property. We also consider this possibility in the model.

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crisis. In spite of the large increase, the number of loans is relatively small when compared to the number of potential borrowers (only two to three percent of eligible borrowers take out a reverse mortgage).

Our model results show that for retirees who derive utility benefits from remaining in the same house reverse mortgages can be beneficial, but for the empirically observed distributions of housing and financial wealth, and the financial terms of reverse mortgages, including both up-front and on-going costs, the model generates very limited demand for these products. And their demand is even lower among retirees who do not value property maintenance as highly as potential buyers of the property.

In the second part of the paper our focus is more normative. We use our model to investigate how the costs and terms of reverse mortgages affect their demand, how to design them so that they are more beneficial to retirees, and at the same time allowing lenders and other market participants to break-even. To be more specific, in our baseline analysis we model the features of the U.S. reverse mortgage market and in particular of those contracts that are originated under the Home Equity Conversion Mortgage (HECM) program insured by the FHA. Such program insulates lenders against the risk of house price declines at a cost that is passed on to borrowers under the form of an insurance premium and of a higher interest rate. The program also imposes limits on the maximum amount that can be borrowed against the house.

Thus in our analysis we model the cash-flows received by the lenders and by the U.S. government, as well as the risks that they face. But we also consider alternative contract parameters and features. In this respect it is useful to compare them to the U.K. reverse mortgages available, which do not receive government guarantees. We evaluate the products bearing in mind their complexity and requirements, since there is evidence that retirees may find it difficult to understand the different features of reverse mortgages and feel a certain reluctance to buy them (Davidoff, Gerhard and Post, 2014).3

Our calculations show that the present value of the cash-flows received by the insurance agency are negative, so that the government is effectively subsidizing reverse mortgages. This is an important point also made in Davidoff (2014), who uses simulation results in a continuous time setting to illustrate the risks of the program to the government. More generally, we use our model to quantitatively evaluate the different mortgage terms, costs and features, and how they impact the demand for reverse mortgages. We show how a reduction in their requirement and costs, including a reduction in the insurance premium, accompanied by a reduction in borrowing limits, may make reverse mortgages more appealling to a wider number of individuals, while at the same time generating positive expected cash-flows for

3This analysis focuses on the design and the terms of reverse mortgage loans. Our objective is to investigate the benefits and disadvantages of certain reverse mortgage features, in the context of a realistically parameterized model. We do not try to solve for the optimal reverse mortgage contract among the set of all possible contracts (Piskorski and Tchistyi, 2010).

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lenders and the insurance agency. Our analysis shows that a higher insurance price, without additional restrictions on loan limits, is a fairly ineffective tool for limiting the losses of the insurance agency.

Our paper is related to the previously mentioned literature on the motives for dissaving during retirement. In addition it is closely related to the papers that study reverse mortgages. Early important contributions include Mayer and Simons (1994) and Caplin (2002). More recent papers include Davidoff (2014) and Hanewald, Post and Sherris (2014). One dimension along which our paper differs from these is in trying to match the patterns observed in the HRS data. In this respect our paper is closer to that of Telyukova and Nakajima (2014). They also solve study reverse mortgage demand in a model parameterized using these data. However, we model a larger number of the risks that retirees face, and explicitly model several of the institutional features of reverse mortgage products, the different types of products available, the financial position of lenders and the insurance agency, and we use our model to study product design.

The paper is structured as follows. In section 2 we describe the reverse mortgage products available in the U.S. and compare them to those available in the U.K., including their costs. We also briefly describe some of the recent market dynamics. Section 3 sets up the model and section 4 the parameterization. Section 5 reports the model results, while section 6 focuses on the terms and features of reverse mortgages. The final section concludes.

2 The Products

2.1 The U.S. products

In the U.S. homeowners have access to several financial products designed to release their home equity. Among them are the traditional home equity loans and lines of credit that require future monthly payments, adequate income and credit scores. For this reason they are not accessible to many older retired individuals who do not meet affordability criteria. An alternative product is reverse mortgages. These loans do not require regular interest or principal repayments since the monthly interest is simply added to the previously outstanding loan balance.

In the U.S. reverse mortgage market the vast majority of the contracts are originated under the HECM program insured by the FHA.4 Under the HECM program homeowners are allowed to borrow up to a fraction of the value of their house in the form of an upfront lump-sum or of a line of credit. We will designate these two alternatives by lump-sum and line of credit, respectively. The lump-sum loan is fixed-rate whereas the line of credit alternative is adjustable-rate indexed to the LIBOR.

4For instance, 96% of active loans in the Fiscal Year of 2011 were insured by the FHA.

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For either alternative, the loan becomes due when the borrower sells the house, dies, or moves out. If at this time the proceeds from the house sale are lower than the outstanding loan balance the FHA insurance will cover the difference, so that lenders still receive the outstanding balance. The retiree or his/her heirs are not liable for any shortfall, but they are entitled to the positive difference between the proceeds from the house sale and the loan balance. The most significant loan requirements are that retirees pay property insurance and taxes, and maintain the property in a good state of repair. If retirees fail to do so the loan may become due, and in case of no repayment, the lender has the right to foreclose.

The initial fees of reverse mortgages include a loan origination fee, a mortgage insurance fee and other closing costs. Panel A of Table I reports representative values for these initial costs. There are both fixed and proportional costs. The initial mortgage insurance premium (MIP) is equal to a proportion of the assessed house value and it depends on the first-year loan disbursement. It is equal to 05% of house value for initial loan disbursements lower than 60% of the maximum loan amount, but it increases to 25% of house value for initial loan disbursements higher than this threshold.5 Panel B of Table I reports typical initial loan interest rates on both lump-sum and line of credit reverse mortgages. They include the lender's margin and an annual mortgage insurance premium of 125% paid to the FHA. The index used for the adjustable-rate is the 1-month LIBOR. The total loan rate determines the rate at which the interest on the outstanding loan balance accrues (it is also known as the accrual rate).6 For comparison this table also reports the difference in interest rates between reverse mortgages and standard principal repayment mortgages.7

A second loan rate that is relevant is the expected loan rate. For the line of credit it is equal to 10-year swap rate plus the applicable margin. For the lump-sum option it is simply equal to the initial loan rate (excluding the mortgage insurance premium). The expected loan rate determines (together with the age of the borrower and the assessed house value) the borrowing limit. The values for this rate at the end of April 2014 are reported in the last row of Table I (it is also known as the HECM expected rate).

Figure 2 plots the borrowing limit or the principal limit factor (PLF) for the different loan types as a function of the borrower's age (or of the youngest co-borrower) at the time that the loan is initiated, for the expected loan rates reported in Table I. The limit increases with

5The U.S. values were obtained using the National Reverse Mortgage Lenders Association mortgage calculator. These values are representative since there is some variation in closing costs across States. The calculations were done at the end of April 2014. The calculator is available at

: . We also use this calculator to obtain the representative interest rates and loan limits reported below. 6For the line of credit the loan rate is also used to determine the rate at which the unused portion of the credit limit grows over time. 7For the line of credit we calculate the difference relative to the 1-year ARM, and for the lump-sum mortgage we calculate the difference relative to the 30-year FRM. The mortgage data is from the Federal Reserve.

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the borrower's age and it is higher for the lump-sum than for the line of credit product, since at the time the expected loan rate was lower for the lump-sum than for the line of credit. However, there is an additional restriction, that the first year loan disbursements must be smaller than the maximum between 60% of the maximum loan amount and the mandatory obligations plus 10% of the maximum loan amount.8 Even though this maximum initial loan disbursement restriction applies to both line of credit and lump sum products, it is a more important restriction for the latter since all funds are borrowed up-front. For this reason in Figure 2 we plot the effects of this restriction on the loan limit for the lump-sum mortgage.

2.2 The U.K. products

In the United Kingdom reverse mortgages have also been available for a number of years. Similarly to the U.S. they are lifetime mortgages that become due when the borrower dies, sells his house or moves out, and they include lump-sum and line of credit alternatives. Although there are several differences relative to the U.S. products, the most significant is that the U.K. products do not receive government guarantees. Lenders provide borrowers with a no negative equity guarantee, so that private providers bear the risk that at loan termination the value of the house may be lower than the outstanding loan balance. In Tables I we report the initial costs and interest rates for representative U.K. products.9 The U.K. products tend to have lower initial costs than their U.S. counterparts but higher loan interest rates, also when compared to the interest rate on standard principal repayment mortgages.

Figure 2 plots typical maximum loan-to-value (LTV) for the U.K. reverse mortgages.10 They are considerable lower than the borrowing limits for the U.S. products, particularly so for younger borrowers. Another interesting difference is that even though in the U.K. the interest rate for the line of credit alternative is lower than for the lump-sum loan, the maximum LTV is higher for the latter. In equilibrium mortgage costs will reflect the riskiness of the loans and of the pool of borrowers who select each type of mortgage. In other words, mortgage characteristics will reflect and explain mortgage selection by heterogeneous borrowers.

8The mandatory obligations include initial loan costs (and HECM counseling), delinquent Federal debt, amounts required to discharge any existing liens on the property, funds to pay contractors who performed repairs as a condition of closing, and other charges authorized by the Secretary.

9These data are obtained from Aviva, a large publicly traded insurance company, and one of the main providers in the U.K. reverse mortgage market.

10The values reported are obtained from Aviva, with loan interest rates equal to those reported in Table I. In the U.K. there are small variations across lenders in maximum LTV.

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2.3 The recent experience

With respect to mortgage characteristics and selection, it is interesting to briefly consider the recent U.S. experience. The products described above, the associated costs and borrowing limits refer to those in existence in April 2014. But over the years there have been a number of changes to the HECM program products and requirements.11 Overall, the size of the U.S. reverse mortgage market is relatively small. Only two to three percent of eligible homeowners take out a reverse mortgage. The annual number of new contracts reached a peak of 115,000 in 2009 but this number declined to 72,000 in 2011, before increasing again in 2014 (Figure 1).

With respect to mortgage type, in 2008 the proportion of contracts of the lump-sum type was only two percent. By 2010 their proportion had increased to 70 percent (Figure 1).12 From 2010 onwards there was a large increase in the number of borrowers who were unable to meet the taxes and insurance payments on their properties required by the reverse mortgage contract, and who were forced to default. These property charge defaults were much higher for borrowers who had chosen the lump-sum alternative. At the same time several of the larger reverse mortgage providers decided to withdraw from the originations market.13

As a response to the higher defaults of lump-sum mortgages the U.S. Department of Housing and Urban Development (HUD) implemented a number of product changes, focused mainly on the insurance premia and borrowing limits. In January 2013 it announced the consolidation of the pricing options and borrowing limits for fixed-rate lifetime mortgages. This effectively meant that only a "saver" product characterized by lower initial mortgage insurance premium (MIP) and lower borrowing limits would be available.14

In September of 2013 there was a further consolidation of products offerings, and adjustment of insurance premia and borrowing limits (Mortgagee Letter 2013-27). The initial insurance premium was set at 05% of the assessed house value and the ongoing annual insurance premium at 125% of the loan outstanding, both for the fixed rate and the adjustable rate mortgages, provided that first-year loan disbursements were lower than 60% of the maximum loan amount. Otherwise the initial insurance premium would increase to 25%. The

11The mortgagee letters describing the changes are available at : ? = . We will not attempt to describe all the changes, but we will focus on those that are more relevant for the analysis. 12The data reported in this paragraph are from the Fiscal Report to Congress on Reverse Mortgages, Consumer Financial Protection Bureau, June 2012. 13The Bank of America withdrew in February 2011 followed by Wells Fargo in June of the same year, and by MetLife in April of 2012. In a statement Wells Fargo said it was leaving the business as a result of "unpredictable home values." There have however been suggestions that the reputational risk arising from foreclosing on retirees in property charge defaults was a more important concern. 14For the adjustable-rate mortgages both a saver and a standard product with higher MIP and borrowing limits would be offered (Mortgagee Letter 2013-01).

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